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mattbaker.blog | ||
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xorshammer.com
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| | | | | There are a number of applications of logic to ordinary mathematics, with the most coming from (I believe) model theory. One of the easiest and most striking that I know is called Ax's Theorem. Ax's Theorem: For all polynomial functions $latex f\colon \mathbb{C}^n\to \mathbb{C}^n$, if $latex f$ is injective, then $latex f$ is surjective. Very... | |
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alanrendall.wordpress.com
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| | | | | In a previous post I discussed the Brouwer fixed point theorem and I mentioned the fact that it applies to any non-empty closed bounded convex subset of a Euclidean space, since a subset of this kind is homeomorphic to a closed ball in a Euclidean space. However I did not prove the latter statement. I... | |
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njwildberger.com
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| | | | | Our paper "A Hyper-Catalan Series Solution to Polynomial Equations, and the Geode" is now available at Taylor and Francis Online. It will appear next month in print form in the American Mathematical Monthly. Here is the link to the paper: https://www.tandfonline.com/doi/full/10.1080/00029890.2025.2460966 From the Abstract: The Catalan numbers?? ??count the number of subdivisions of a polygon... | |
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kristalcantwell.wordpress.com
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| | | Mini-polymath 4 has started. It is based on question 3 of the IMO. The research thread is here. There is a wiki here. | ||
